CFA Level II · CFA Level II Exam

Introduction to Commodities and Commodity Derivatives: formula sheet

Full chapter guide

Key formulas

Commodity valuation basis: Price = f(supply, demand, storage cost, convenience yield); no discounted cash flow; Commodities have no cash flows, so equity and bond valuation methods do not apply directly.
Futures price with carry costs (cost-of-carry idea): F₀ ≈ S₀ × (1 + r) + storage costs − convenience yield; Higher storage cost pushes futures above spot; higher convenience yield pushes them down. Treat as a conceptual relationship unless the vignette gives a formula.
Convenience yield effect: Higher convenience yield → futures price lower relative to spot; Strong near-term need for physical supply favours holders of the physical commodity.
Futures gain or loss (long): Gain = (Settlement price − Previous settlement price) × Contract size × Number of contracts; A short position has the opposite sign. Used for daily marking to market.
Cash settlement amount: Payment = (Final reference price − Contract price) × Quantity; Positive means the long receives. Negative means the long pays.
Fixed-for-floating swap payment: Net payment to fixed payer = (Floating price − Fixed price) × Notional quantity; Positive means the fixed payer receives. Only the net amount is paid.
Margin rule: Margin call if account balance < maintenance margin; restore to initial margin; Check the vignette for whether the top-up is to initial or maintenance level.
Cost-of-carry futures price (with convenience yield): F₀ = S₀ × (1 + r)^T + FV(storage costs) − FV(convenience yield); Conceptual form. Storage and interest raise F₀. Convenience yield lowers it. Use the exact form the vignette gives.
Contango: Longer-dated futures price > nearer-dated futures price; Upward-sloping curve. Defined by shape only, not by expected price direction.
Backwardation: Longer-dated futures price < nearer-dated futures price; Downward-sloping curve. Usually linked to high convenience yield.
Net cost of carry condition: Contango if r + storage > convenience yield; backwardation if convenience yield > r + storage; Compare the two sides on the same time basis, such as annualised rates.
Roll yield sign: Backwardation: roll yield > 0 for a long position; contango: roll yield < 0; Assumes the long rolls from the near contract to the next, with the spot price unchanged.
Theory of storage (cost of carry with convenience yield): F₀ = S₀ × (1 + r + c − y); Rates form: r, c and y are rates for the same period (interest, storage cost, convenience yield). In money terms, the discrete form is F₀ = S₀ × (1 + r) + FV(storage costs) − FV(convenience yield). Do not mix the two forms. Continuous form: F₀ = S₀ × e^((r + c − y)T). Backwardation (F₀ < S₀) needs y > r + c.
Insurance theory (normal backwardation): Futures price < Expected future spot price; Hedgers are net short, speculators are net long and earn a positive risk premium.
Hedging pressure: net short hedgers: Futures price < Expected future spot price; Speculators are long and earn a positive premium.
Hedging pressure: net long hedgers: Futures price > Expected future spot price; Speculators are short. This is normal contango. The long side earns a negative premium.
Convenience yield and inventory: Low inventory → high convenience yield → backwardation if y > r + c; High inventory → low convenience yield → contango; Convenience yield is a benefit of holding the physical commodity, not of holding the futures.
Total return: Total return = spot return + roll return + collateral return; Approximation used in the curriculum. Returns are for the same period.
Spot return: Spot return = (S1 − S0) ÷ S0; Based on the spot price, not the futures price.
Roll return (per roll): Roll return = (near-term futures price − farther-term futures price) ÷ near-term futures price; Positive in backwardation, negative in contango. Sign convention is for a long position.
Roll return from total futures change: Futures price return ≈ spot return + roll return; The price change on the rolled futures position, excluding collateral.
Collateral return: Collateral return = interest rate on collateral × period fraction; Scale an annual rate to the holding period.
Commodity index return: Total return = spot return + roll return + collateral return; Futures-based indexes earn all three. Roll return is positive in backwardation and negative in contango.
Production weighting (S&P GSCI): Weight ∝ world production quantity × futures price; Energy ends up with the largest weight. Weights shift as prices change.
BCOM weighting rule: Weights based on liquidity and production, with caps on sector and single-commodity weights; Caps limit concentration, giving a more diversified index than S&P GSCI.
Equity-linked exposure: Producer equity return ≠ commodity price return; Equities add operating leverage, hedging and market beta, so tracking is loose.

Quick revision

Commodities are real assets with no cash flows, so returns come from price changes and the futures structure.
Contango: futures prices are above spot, and longer-dated futures are higher than shorter-dated ones.
Backwardation: futures prices are below spot, and longer-dated futures are lower than shorter-dated ones.
Rolling a long position in contango usually gives negative roll yield, since you buy the higher-priced contract later.
Rolling a long position in backwardation usually gives positive roll yield.
A high convenience yield pushes the curve toward backwardation; high storage costs push it toward contango.
Total return on a fully collateralised futures position = spot return + roll yield + collateral return.
Insurance theory (normal backwardation in the Keynes sense) implies futures prices are below expected future spot prices, because hedgers pay a premium to speculators, so long positions earn a risk premium. This is a statement about futures versus expected spot, which is distinct from the curve shape comparing futures with current spot.
The theory of storage links the curve to inventory levels, storage costs and convenience yield.
Index design choices, such as weights and roll rules, can change returns even when the same commodities are held.
Investors can access commodities through futures, funds, ETFs, equities of producers or notes, each with different tracking risks.
Read the contract months in the vignette carefully, because roll yield depends on which two contracts you compare.

Common mistakes

Valuing a commodity using discounted cash flows. Fix: Remember commodities produce no cash flows. Think supply, demand and cost of carry.
Treating all commodities as equally storable. Fix: Check storability by sector. Gold stores easily; electricity, natural gas and livestock do not.
Saying futures have no credit risk at all. Fix: Say credit risk is greatly reduced through margin and daily settlement, not eliminated.
Treating a forward as marked to market daily. Fix: Daily marking is a futures feature. A forward usually settles only at maturity.
Saying contango means prices are expected to rise. Fix: Contango is only a shape. Theory says it reflects carry costs, and the curve does not predict spot prices by itself.
Adding convenience yield to the futures price. Fix: Convenience yield is a benefit to holders of the physical, so it lowers the futures price relative to spot.
Treating backwardation as the same thing in all three theories. Fix: Always ask what the futures price is being compared with. Expected spot relates to the risk premium theories. Spot price relates to the storage theory.
Saying insurance theory allows a negative premium for the long side. Fix: Insurance theory assumes hedgers are net short, so the long speculator earns a positive premium. The possibility of a negative premium comes from hedging pressure.
Getting the roll return sign wrong in contango. Fix: You sell the near contract and buy the far one. Paying more for the far contract is a cost, so roll return is negative.
Dividing the roll difference by the far price. Fix: The curriculum measures roll return relative to the near-term price: (near − far) ÷ near.

Exam tips

Read the vignette for storability, seasonality and cyclicality cues, as they usually point to the answer.
Be ready to contrast commodities with equities and bonds in one line: no cash flows, supply and demand driven.
Do not overstate diversification or inflation hedging; pick answers that say 'may' or 'can'.
Link sector traits to futures curve behaviour, since later topics build on this.
Do not spend long on a question; there is no penalty for a wrong answer, so always select an option.
Read who the party is and why it trades before choosing hedger or speculator.
Check the sign of every gain or loss, and whether the position is long or short.
Expect questions contrasting futures with forwards on credit risk, liquidity and customisation.